Analog sticks - when they are moved - have a range between - for example - 0 to 100 (in reality it's closer to 0 to 255 but it's the same point).

If you put the deadzone to higher than 0, movement won't be sent to the game at all unless the stick is moved that much.

i.e. it's mainly for unstable/faulty controllers. I use 0 unless I notice a hardware problem. Games have their own deadzone usually anyway (e.g. a character may not move at all unless the stick is moved for 10-20% for example).

Range is probably to workaround unsupported controllers or faulty controllers that have wonky max ranges. For example the genuine nunchuk had a max at lower than 255 but some knockoffs had it there and that can mess up software (in that case a lower than 100% Range may help)

Not sure what button threshhold is. It's a cryptic phrase. Maybe a 'deadzone' for analog buttons. Ask petergov (the main dev of controls) on discord to get an exact answer.

update: If you use the calibration feature, you may be able to get away with some controllers initially reporting wonky ranges.